Search results for: integral transformation

Authors: Aouachria Mekki

Abstract:

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

Keywords: Path integral, formalism, Propagator.

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Authors: Yang Zhong, Mei-jie Xu

Abstract:

To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. So the dynamic change of parameter in asphalt mixture should be taken into consideration when theoretical analysis is taken out.

Keywords: Asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress.

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Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

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Authors: Nizami Mustafa, C. Ardil

Abstract:

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

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Authors: S. Sutor, R. Röhr, G. Pujolle, R. Reda

Abstract:

This paper presents a highly efficient algorithm for detecting and tracking humans and objects in video surveillance sequences. Mean shift clustering is applied on backgrounddifferenced image sequences. For efficiency, all calculations are performed on integral images. Novel corresponding exponential integral kernels are introduced to allow the application of nonuniform kernels for clustering, which dramatically increases robustness without giving up the efficiency of the integral data structures. Experimental results demonstrating the power of this approach are presented.

Keywords: Clustering, Integral Images, Kernels, Person Detection, Person Tracking, Intelligent Video Surveillance.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: A. Zerarka, A. Soukeur, N. Khelil

Abstract:

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.

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Authors: S. K. Tomar, R. Prasad, S. Panda, C. Ardil

Abstract:

Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Discrete System, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation, Particle Swarm Optimization, Integral Squared Error.

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented.

Keywords: Algebras over integral domains, Alexandroff topology, immediate neighbors, integral domains.

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Authors: M. Zarebnia, S. Khani

Abstract:

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

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Authors: Salma Faraj Ramadan, Maslina Darus

Abstract:

In this paper we define generalized differential operators from some well-known operators on the class A of analytic functions in the unit disk U = {z ∈ C : |z| < 1}. New classes containing these operators are investigated. Also univalence of integral operator is considered.

Keywords: Univalent functions, integral operators, differential operators.

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Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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Authors: Tiexin Wang, Sebastien Truptil, Frederick Benaben

Abstract:

Model transformation, as a pivotal aspect of Modeldriven engineering, attracts more and more attentions both from researchers and practitioners. Many domains (enterprise engineering, software engineering, knowledge engineering, etc.) use model transformation principles and practices to serve to their domain specific problems; furthermore, model transformation could also be used to fulfill the gap between different domains: by sharing and exchanging knowledge. Since model transformation has been widely used, there comes new requirement on it: effectively and efficiently define the transformation process and reduce manual effort that involved in. This paper presents an automatic model transformation methodology based on semantic and syntactic comparisons, and focuses particularly on granularity issue that existed in transformation process. Comparing to the traditional model transformation methodologies, this methodology serves to a general purpose: crossdomain methodology. Semantic and syntactic checking measurements are combined into a refined transformation process, which solves the granularity issue. Moreover, semantic and syntactic comparisons are supported by software tool; manual effort is replaced in this way.

Keywords: Automatic model transformation, granularity issue, model-driven engineering, semantic and syntactic comparisons.

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Authors: Pan Cheng, Jin Huang, Guang Zeng

Abstract:

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

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Authors: Farid Saeidi, Serkan Dag

Abstract:

In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, variable fiber spacing, thermoelasticity, t-stress, finite element method, fibrous composite.

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Authors: Sinnakkrishnan Perumal, Nitish Pandey

Abstract:

Business transformation initiatives are required by any organization to jump from its normal mode of operation to the one that is suitable for the change in the environment such as competitive pressures, regulatory requirements, changes in labor market, etc., or internal such as changes in strategy/vision, changes in the capability, change in the management, etc. Recent advances in information technology in automating the business processes have the potential to transform an organization to provide it with a sustained competitive advantage. Process constitutes the skeleton of a business. Thus, for a business to exist and compete well, it is essential for the skeleton to be robust and agile. This paper details “transformation" from a business perspective, methodologies to bring about an effective transformation, process-based transformation, and the role of services computing in this. Further, it details the benefits that could be achieved through services computing.

Keywords: Business Transformation, Services Oriented Architecture, Business Processes, Process-based Transformation.

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Authors: F. Amin, S. Feizi

Abstract:

Big data has the potential to improve the quality of services; enable infrastructure that businesses depend on to adapt continually and efficiently; improve the performance of employees; help organizations better understand customers; and reduce liability risks. Analytics and marketing models of fixed and mobile operators are falling short in combating churn and declining revenue per user. Big Data presents new method to reverse the way and improve profitability. The benefits of Big Data and next-generation network, however, are more exorbitant than improved customer relationship management. Next generation of networks are in a prime position to monetize rich supplies of customer information—while being mindful of legal and privacy issues. As data assets are transformed into new revenue streams will become integral to high performance.

Keywords: Big Data, Next Generation Networks, Network Transformation.

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Authors: Ayman El-Garem, Riham Adel

Abstract:

Digital transformation is about identifying the necessary changes of the entire business model, rethinking how to transform the traditional operations into digital ones that can create better value to its customers. Efforts are common across industries, but they often fail due to a lack of understanding of the factors required to focus on and change to be able to embark in digital transformation successfully. Further research is required to bridge the knowledge gap between academia and industry to support companies starting their digital transformation journey. To date there is no consensus on digital transformation key success factors. Therefore, the aim of this paper is to identify the success factors in digital transformation journey, throughout conducting a systematic literature review of 134 peer-reviewed articles to get better insights regarding the research progress in this field.  After completing the systematic literature review it will be followed by Delphi study to get experts consensus on the most significant factors affecting digital transformation implementation. The findings indicate that organizations undergoing digital transformation should focus mainly on (1) well managed digital transformation activities; (2) digital business strategy; (3) supportive culture; (4) top management support; (5) organizational change capabilities.

Keywords: Digital transformation, key success factors, literature review, Delphi study.

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

The Choquet integral is a tool for the information fusion that is very effective in the case where fuzzy measures associated with it are well chosen. In this paper, we propose a new approach for calculating fuzzy measures associated with the Choquet integral in a context of data fusion in multimodal biometrics. The proposed approach is based on genetic algorithms. It has been validated in two databases: the first base is relative to synthetic scores and the second one is biometrically relating to the face, fingerprint and palmprint. The results achieved attest the robustness of the proposed approach.

Keywords: Multimodal biometrics, data fusion, Choquet integral, fuzzy measures, genetic algorithm.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: Frequency transformation, Bilinear z-transformation, Pre-warping frequency, Digital filters, Analog filters, Pascal’s triangle.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Due to the increasing penetration of wind energy, it is necessary to possess design tools that are able to simulate the impact of these installations in utility grids. In order to provide a net contribution to this issue a detailed wind park model has been developed and is briefly presented. However, the computational costs associated with the performance of such a detailed model in describing the behavior of a wind park composed by a considerable number of units may render its practical application very difficult. To overcome this problem integral manifolds theory has been applied to reduce the order of the detailed wind park model, and therefore create the conditions for the development of a dynamic equivalent which is able to retain the relevant dynamics with respect to the existing a.c. system. In this paper integral manifold method has been introduced for order reduction. Simulation results of the proposed method represents that integral manifold method results fit the detailed model results with a higher precision than singular perturbation method.

Keywords: Wind, Reduced Order, Integral Manifold.

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Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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